Inhomogeneous and anisotropic field theory of gravitation and electromagnetism: Fundamentals of relativistic unification

A relativistic field theory of inhomogeneous and anisotropic matter and radiation with a mathematical manifold structure should account for an impersonal picture of the world and contact with physical observables. To incorporate in the theory the interacting nature of microscopic and macroscopic constituents presents philosophical, physical, and mathematical issues. Such a field theory of gravitation and electromagnetism can be motivated by averaging the constituents of fine-grained space-time regions, but a gauge-independent theory of the averaged intrinsic tensor fields defined on a coarse-grained mathematical manifold with structure can only be deduced and closure of the fields established by a relativistic theory of constitutive equations. Figs 3, Refs 12.